UPDATE 3-Murdoch's UK arm denies phone hacking allegations

* News International denies phone hacking allegations

* Prosecutors, MPs to look into phone hacking by media

(Adds background, changes dateline)

By Kate Holton and Robert MacMillan

LONDON/NEW YORK, July 10 (Reuters) - The British newspaper arm of Rupert Murdoch's News Corp denied on Friday allegations its journalists had hacked into the phones of thousands of public figures, following days of damning headlines.

The Guardian newspaper reported earlier this week News International (NWSA.O) had already paid 1 million pounds ($1.6 million) to settle court cases with three people -- including soccer executive Gordon Taylor -- whose phones were accessed.

But the report also suggested journalists at the mass-selling Sunday tabloid, the News of the World, had conspired to hack into the phones of thousands of public figures from politicians to celebrities and sporting bosses.

News International finally released a statement on Friday, saying that after a full examination and apart from two already acknowledged cases, the allegations were not true.

"It is untrue that officers found evidence of News Group staff, either themselves or using private investigators, hacking into "thousands" of mobile phones," the statement said.

"It is untrue that News of the World executives knowingly sanctioned payment for illegal phone intercepts. All of these irresponsible and unsubstantiated allegations against News of the World and other News International titles and its journalists are false."

The Guardian allegations grabbed headlines in Britain, where the tabloid press fiercely compete through major scoops on sex, scandal and "showbiz exclusives".

Actors Jude Law and Gwyneth Paltrow, Australian model Elle Macpherson and former British deputy Prime Minister John Prescott were among those targeted, the Guardian reported.

News Corp chief Rupert Murdoch, who was attending the Allen & Co media conference in Sun Valley, Idaho, refused to address reporter questions about the matter.

The Guardian report followed the jailing in 2005 for phone hacking of News of the World royal reporter Clive Goodman and a private investigator Glen Mulcaire, which in turn had followed a long police investigation.

News International said apart from these two men, the only other case connecting reporters with gaining evidence from a person's voicemail emerged in April 2008, during the course of the Taylor litigation.